Find the solution set of the following quadratic equations by completing the square. 1.) x^2 – 10x + 1 = 0 2.) 4x^2 – 8x = 1

Question

Find the solution set of the following quadratic equations by completing the square.

1.) x^2 – 10x + 1 = 0
2.) 4x^2 – 8x = 12

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Trúc Chi 4 years 2021-08-15T16:19:40+00:00 1 Answers 7 views 0

Answers ( )

  1. sori
    0
    2021-08-15T16:20:43+00:00
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    Answer:

             1)  \bold{x=2\sqrt6+5\quad\ \vee\quad x=-2\sqrt6+5}

              2)    \bold{x=3\quad\vee\quad x=-1}

    Step-by-step explanation:

    1)

      x^2 - 10x + 1 = 0\\\\x^2 - 2\cdot x\cdot5 +5^2-5^2 + 1 = 0\\\\(x-5)^2-25+1=0\\\\(x-5)^2=24\\\\x-5=\sqrt{24}\qquad\vee\qquad x-5=-\sqrt{24}\\\\ x=2\sqrt6+5\qquad\vee\qquad x=-2\sqrt6+5

    2)

    4x^2-8x=12\\\\x^2-2x=3\\\\x^2-2\cdot x\cdot1+1^2-1^2=3\\\\(x-1)^2-1=3\\\\(x-1)^2=4\\\\x-1=2\qquad\vee\qquad x-1=-2\\\\x=3\qquad\vee\qquad x=-1

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )